Question

The no. of diagonals drawn from one vertex of a polygon of n side is-------------------.
a)n-1
b)n-2
c)n-3
d)n

Answer 1

Answer:

c)n-3

Step-by-step explanation:

⇒  A diagonal is a segment that connect two non-consecutive vertices in polygon.

⇒  The number of diagonal in a polygon that can be drawn from any vertex in polygon is three less than the number of sides.

⇒  Let n be the number sides in polygon.

⇒  So, the number of diagonals drawn from the vertex of polygon of n sides is (n−3).

Answer 2

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.